In today's rapidly evolving telecommunications infrastructure, optical communications systems fulfill one of the most important roles of very high speed and high bandwidth data transmission over both long and short distances (anywhere from a few hundreds of meters in datacenters to thousands of kilometers over transatlantic and submarine fibers). In order to meet the demands of high throughput over legacy installed fiber, sophisticated transmit and receive signal processing algorithms are constantly being introduced as potential solutions to be implemented in communications hardware.
In conventional modulation schemes, a “modulation symbol” represents a group of bits to be transmitted and is defined as a unique combination of phase shifts and power levels, and a “constellation” diagram represents the location (or “constellation point”) of each modulation symbol in an x-y scatter diagram. The number of possible modulation symbols available for any given sampling instant is a function of the number of distinct phase shifts and power levels. The set of symbols for any given modulation scheme is sometimes called the “modulation symbol alphabet.”